Modular curved surface space structures

ABSTRACT

A plurality of mathematically interrelated modular structures are disclosed which are based on a series of minimal surfaces bounded by skewed polygons. Some six basic modules are described which are capable of being interconnected in various combinations to form finite volume enclosing structures. Appropriately scaled, the modules could be used as structure toys, to create playground equipment or, for the construction of habitible structures. Utilizing these structural modules, it is possible to construct large assemblies having parallel planar structures within the enclosed space which could be considered floors and ceilings of multilevel structures.

United States Patent [1 1 Pearce 1 Dec. 16, 1975 154] MODULAR CURVED SURFACE SPACE STRUCTURES [75] Inventor: Peter J. Pearce, Studio City, Calif.

[73] Assignee: Synestructics, Inc., Chatsworth,

Calif.

[22] Filed: May 13, 1974 [21] Appl. No.: 469,415

Related US. Application Data [62] Division of Ser. No. 216,488, Jan. 10, 1972,

abandoned.

[52] 11.8. C1. 52/82; 52/81; 52/86; 52/D1G. 10

[51] Int. Cl. E04B 1/32 [58] Field of Search 52/80, 81, 82, 86

[56] References Cited UNITED STATES PATENTS 2,891,491 6/1959 Richter 52/81 2,928,360 3/1960 Heine 3,092,932 6/1963 Wilson 52/80 3,206,895 9/1965 De Ridder 3,445,970 5/1969 Nelson 3,461,626 8/1969 Aitken 3,543,455 12/1970 Walsh 3,568,381 3/1971 Hale 3,663,347 5/1972 Schoen Dl99,733 12/1964 Hastings D204,239 4/1966 Upor 52/81 FOREIGN PATENTS OR APPLICATIONS 1,262,098 4/1961 France 52/80 966,344 7/1957 Germany 52/80 967,000 9/1957 Germany 52/80 OTHER PUBLICATIONS Surfaces Minimales Et. Polyedres-Selles, pp. 8996, LArchitecture DAujourd Hui, May 1969. Mathematical Models, by Cundy and Rollett, pp. 100-105, 158, 159 and 178-181, 1961.

Primary ExaminerErnest R. Purser Assistant ExaminerHenry Raduazo Attorney, Agent, or FirmMarvin H. Kleinberg [57] ABSTRACT A plurality of mathematically interrelated modular structures are disclosed which are based on a series of minimal surfaces bounded by skewed polygons. Some six basic modules are described which are capable of being interconnected in various combinations to form finite volume enclosing structures. Appropriately scaled, the modules could be used as structure toys, to create playground equipment or, for the construction of habitible structures. Utilizing these structural modules, it is possible to construct large assemblies having parallel planar structures within the enclosed space which could be considered floors and ceilings of multilevel structures.

16 Claims, 70 Drawing Figures US. Patent Dec. 16, 1975 Sheet 1 of 17 3,925,941

U.S. Patent Dec. 16,1975 Sheet2of 17 3,925,941

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US. Patent Dec. 16, 1975 Sheet 7 of 17 3,925,941

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MODULAR CURVED SURFACE SPACE STRUCTURES This is a division of application Ser. No. 216,488, filed Jan. 10, 1972 now abandoned.

The present invention relates to modular structural elements and, more particularly, a series of saddle type curved surface polygonal modules which can combine and repeat in various add mixtures to form a collection of spatial structures capable of efficiently enclosing and subdividing space.

BACKGROUND OF THE INVENTION From time to time, in the prior art, suggestions have been made that closed finite polyhedra made up of saddle shaped polygons spanned by minimal surfaces are possible and M. Burt has, in a book entitled Spatial Arrangements and Polyhedra With Curved Surfaces and Their Architectural Applications, published by Technion, Haifa, Israel, in November of 1966, described a set of polyhedra. Three of Burts polyhedra can be used to form unary space filling systems. Some of the others are capable of combinations which provide spans, trusses and other architectural elements.

Others, have in recent years, proposed minimal curved surfaces for use as core structures, such as is taught in the US. Pat. No. to Robb, 3,227,598; or in walls, as is shown in Hauer, US. Pat. No. 3,038,278. Similarly, the US. Pat. No. to Hale, 3,525,663 teaches a cellular core structure using curved surfaces.

According to the present invention, a plurality of curved surface modules are derived as approximations of surfaces of least area, relative to closed polyogonal perimeters. Each module starts with a non-planar skew polygon. When a minimal surface is bounded by the skew polygon, the result is a saddle like, smooth surface which tends to optimize distribution of stress.

Utilizing the concepts of the present invention, a fundamental set of six primary interrelated curved surface modules has been derived. The set includes an octagonal figure, two hexagonal figures, one of which can be modified into pentagonal shape, and three dodecagonal figures. The included angles between adjacent edges of the polygons tend to be either 90, 120, or 135. The dihedral angles between intersecton planes of the skew polygons are either 125 16 or 109 28'. Within these constraints, the edge lengths can be established for a given set of modules.

Sets of modules can be assembled and interconnected to form structures which can enclose space as simple finite polyhedra, or as continuous structures capable of virtually indefinite extension. The structures thus created would include curved space labyrinths having complementary tunnel regions which are identical or congruent. Certain of these spatial configurations are adapted to employ, in addition to the curved surface structural modules, planar, regular polygons.

In yet other embodiments, adapted for use in playground equipment, simple connectors have been devised to couple modules together into appropriate structures. Such techniques include plastic hinged joints as well as hingeable flanged couplers, channel members and the like.

In the preferred embodiment of the present invention, the individual modules will be made from rigid or semi-rigid materials so as to resist both tension and compression loads. A plurality of polygonal units can be arranged so that a single continuous membrane can be substituted for a series of interconnected individual modules in a minimal surface which conforms to the several polygons.

A triangulated skeletal approximation can be derived from each curved surface module. Such an approximation would utilize the teachings of a copending application of the inventor entitled Minimum Inventory Maximum Diversity Building System, filed Aug. 30, 1971, Ser. No. 176,220. Such structures would utilize strut members to form the perimeter of the module, and other strut members would be used to triangulate the structure to afford structural rigidity.

In another embodiment, an alternative triangulated approximation can be created from a plurality of planar, triangular elements replacing the skeletal strut members. As is taught in the copending Pearce application, supra, a plane triangular plate would be the full structural equivalent of a skeletal frame of the same shape or outline.

It is, therefore, an object of the present invention to provide a set of minimal surface, polygonal modules that are capable of being assembled into integral, selfsupporting structures.

It is an additional object of invention to provide a family of related, polygonal modules that can be assembled into novel and challenging play structures.

It is a further object of invention to provide a family of related, polygonal modular shapes that can be utilized as a construction toy.

The novel features which are believed to be characteristic of the invention, both as to organization and method of operation, together with further objects and advantages thereof will be better understood from the following description considered in connection with the accompanying drawings in which several preferred embodiments of the invention are illustrated by way of example. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention.

FIG. 1 is a perspective view of a multi-story structure composed of modules according to the present invention;

FIG. 2, including FIGS. 2a through 2e, inclusive, relates to an octagonal curved surface module according to the present invention in which FIG. 2a is a per spective view of the intersecting planes which help define the module; FIG. 2b is a perspective view of a minimum surface module so defined; FIG. 20 is a perspective view of a triangulated planar approximation of the module; FIG. 2d is a top view of the module triangulated by skeletal struts; and FIG. 2e is a modification of the module wherein arcs replace certain of the linear edges.

FIG. 3, including FIGS. 3a through 3e, inclusive, relates to a hexagonal curved surface module according to the present invention in which FIG. 3a is a perspective view of the intersecting planes which help define the module; FIG. 3b is a perspective view of a minimum surface module so defined; FIG. 3c is a perspective view of a triangulated planar approximation of the module; FIG. 3d is a top view of the module triangulated by skeletal struts; and FIG. Se is a modification of the module wherein arcs replace certain of the linear edges.

FIG. 4, including FIGS. 4a through 4/1, inclusive, relates to an alternative hexagonal curved surface module according to the present invention in which FIG. 4a is a perspective view of the intersecting planes which help define the module; FIG. 4b is a perspective view of a minimum surface module so defined; FIG. 40 is a perspective view of a triangulated planar approximation of the module; FIG. 4d is a top view of the module triangulated by skeletal struts; FIG. 4e is a modification of the module wherein arcs replace certain of the linear edges; FIG. 4f is a perspective view of the module of FIG. 4b modified to a pentagonal shape; FIG. 4g is a perspective view of a triangulated planar approximation of the modified module; and FIG. 411 is a top view of the modified module triangulated by skeletal struts.

FIG. 5, including FIGS. 5a through 5f, inclusive, relates to a dodecagonal curved surface module according to the present invention in which FIG. 5a is a perspective view of the intersecting planes which help define the module; FIG. 5b is a perspective view of a minimal surface module so defined; FIG. 50 is a perspective view of a triangulated planar approximation of the module; FIG. 5d is a top view of the module triangulated by skeletal struts; FIG. Se is a modification of the module wherein arcs replace certain of the linear edges; and FIG. 5f is a further modification in which all straight edges are replaced by curves.

FIG. 6, including FIGS. 6a through 6e, inclusive, relates to an alternative, symmetrical dodecagonal surved surface module according to the present invention in which FIG. 6a is a perspective view of the intersecting planes which help define the module; FIG. 6b is a perspective view of the module so defined; FIG. 60 is a perspective view of a triangulated planar approximation of the module; FIG. 6d is a top view of the module triangulated by skeletal struts; and FIG. 6e is a modification of the module wherein arcs replace certain of the linear edges.

FIG. 7, including FIGS. 7a through 72, inclusive, relates to another symmetrical dodecagonal curved surface module according to the present invention in which FIG. 7a is a perspective view of the intersecting planes which help define the module; FIG. 7b is a perspective view of the module so defined; FIG. 7c is a perspective view of a triangulated planar approximation of the module; FIG. 7d is a top view of the module triangulated by skeletal struts; and FIG. 7e is a modification of the module wherein arcs replace certain of the linear edges.

FIG. 8, including FIGS. 8a and 8b, is a structure comprised of the modules of FIGS. 3b and 5b and of the comparable structure comprised of the modules of FIGS. 3e and Se in FIGS. 8a and 8b, respectively;

FIG. 9, including FIGS. 9a and 9b, illustrates structures comprised of the elements of FIGS. 2a, 6b, and 2e, 6e, in FIGS. 9a and 9b, respectively;

FIG. 10, including FIGS. 10a and 10b, illustrates structures comprised of the modules of FIGS. 3b. 4b, and 3e and 4e, in FIGS. 10a and 10b. respectively;

FIG. 11 is a partially exploded view of a complex structure employing units comprised of the modules of FIGS. 2, 3 and 6;

FIG. 12 is a perspective view, partly broken away of a portion of the structure of FIG. 11. containing a plurality of parallel planes suitable as an element of a habitable structure;

FIG. 13 is a perspective view of a more complex structure utilizing components of the present invention;

LII

FIG. 14 is a perspective view. partially broken away, of a portion of the structure of FIG. 13 showing a set of parallel planes in the interior of the structure;

FIG. 15 in an alternative structural combination comprised of the modules FIGS. 3b, 4f of the present invention;

FIG. 16 is a perspective view of a tunnel labyrinth structure comprised of modules of the present invention;

FIG. 17 is a view of a labyrinthine structure comprised of modules of FIG. 5b of the present invention;

FIG. 18 is a perspective view of a labyrinthine structure substantially identical to that of FIG. 17, except that the modules of FIG. 5b utilized in the structure of FIG. 17 have been replaced by the modules of FIG. 5f;

FIG. 19 including FIGS. 19a and 19b, illustrates two alternative configurations of the same labyrinth system comprising modules with straight edges, FIG. 19a, and with curved edges, FIG. 19b,-

FIG. 20 is yet another complex structure employing modules of the present invention;

FIG. 21 including FIGS. 21a through d, inclusive, is a perspective end view of coupling hinges suitable for joining the modules of FIGS. 2 through 7;

FIG. 22 is a top view, of a module according to the present invention having a hinged edge adaptable for interconnecting with other similar modules;

FIG. 23 is a sectional view of the module of FIG. 22 taken along line 23-23 in the direction of the appended arrows;

FIG. 24 including FIGS. 24a through e, inclusive, illustrates the sequential steps of joining modules by clamping edges;

FIG. 25 is a top view of interconnected modules such as are illustrated in FIGS. 3a and 3b;

FIG. 26 is a sectional view of the structure of FIG. 25 taken along the lines 2626 in the direction of the appended arrows:

FIG. 27 is a sectioned view of the structure of FIG. 25 taken along lines 27-27 in the direction of the appended arrows;

FIG. 28 represents the 20 horizontal planar sections of the structure of FIG. 1.

Turning first to FIG. 1, there is illustrated a multistory structure, comprised for the most part of a superstructure which is in turn assembled from surface modules of the present invention. As illustrated, the structure may be considered a 20 story habitable structure in which floor layers span and, subdivide very large volumetric regions created by the super-structure.

As illustrated in FIG. 1, the structure terminates in domes of the type disclosed in the copending application of the present inventor, entitled Minimum Inventory Maximum Diversity Building System, filed Aug. 30, 1971, Ser. No. 176,220. In that application, a building system was disclosed which comprised a plurality of strut members of predetermined dimensions which, when interconnected, provided modular structures using linear frameworks which were triangulated for structural rigidity. Because of the selection of relative sizes of the structural members, dome structures were provided of high volume to weight ratios and of great inherent structural strength and stability.

While it is not essential that such elements of the system of the copending application be employed, they are useful to illustrate the flexibility of the present invention and its ability to accommodate other systems. 

1. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having six edges, one pair of opposing edges and an included edge defining a first plane, a second pair of opposing edges and an included edge defining a second plane; the interior angles of the edges defining said first and second planes being 120*, said first and second planes intersecting at a dihedral angle of 125* 16'', the edges at said intersection of planes joining at 90*.
 2. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having six edges, one pair of opposing edges and an included edge defining a first plane, a second pair of opposing edges and an included edge defining a second plane; the interior angles of the edges defining said first and second planes being 120*, said first and second planes intersecting at a dihedral angle of 125* 16'', the edges at said intersection of planes joining at 90*.
 3. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having eight edges and the interior angles of the vertices each being substantially 120*, one pair of opposing edges defining a base plane, a second pair of opposing edges, together with an included edge, defining a second plane and a third pair of opposing edges, together with an included edge defining a third plane, said second and third planes intersecting said base plane at dihedral angles of substantially 125* 16''.
 4. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having eight edges and the interior angles of the vertices each being substantially 120*, one pair of opposing edges defining a base plane, a second pair of opposing edges, together with an included edge, defining a second plane and a third pair of opposing edges, together with an included edge defining a third plane, said second and third planes intersecting said base plane at dihedral angles of substantially 125* 16''.
 5. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having six edges, a first pair of opposing edges being joined by an included third, coplanar edge at angles of substantially 120* to define a first plane and a second pair of edges being joined by an included sixth coplanar edge at angles of substantially 135* to define a second plane, said first and second planes intersecting at a dihedral angle of substantially 125* 16'', said first and second pair of opposing edges being joined at 90* substantially at the intersection of said planes.
 6. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having six edges, a first pair of opposing edges being joined by an included third, coplanar edge at angles of substantially 120* to define a first plane and a second pair of edges being joined by an included sixth coplanar edge at angles of substantially 135* to define a second plane, said first and second planes intersecting at a dihedral angle of substantially 125* 16'', said first and second pair of opposing edges being joined at substantially 90* at the intersection of said planes.
 7. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having five straight edges, four of the edges intersecting at substantially 90* angles, and the fifth edge joining adjacent edges at substantially 120*, said fifth edge and the two edges adjacent thereto defining a first plane, the remaining two edges defining a second plane, said first and second planes intersecting at a dihedral angle of substantially 125* 16'', the edges at said intersection of said first and second planes joining at substantially 90* angles.
 8. A saddle-like polygonal surface module for definiNg, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having five straight edges, four of the edges intersecting at substantially 90* angles, and the fifth edge joining adjacent edges at substantially 120*, said fifth edge and the two edges adjacent thereto defining a first plane, the remaining two edges defining a second plane, said first and second planes intersecting at a dihedral angle of substantially 125* 16'', the edges at said intersection of said first and second planes joining at substantially 90* angles.
 9. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having 12 edges, four pairs of said edges intersecting at four points to define a first, base plane, each adjacent pair of said points also defining the intersection of said first plane with second, third, fourth and fifth planes at dihedral angles of substantially 125* 16'', said second, third, fourth and fifth planes each being defined by a pair of opposing edges and an included edge, each included edge joining adjacent coplanar edges at 120* and the edges intersecting at said points joining at 90*.
 10. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having 12 edges, four pairs of said edges intersecting at four points to define a first, base plane, each adjacent pair of said points also defining the intersection of said first plane with second, third, fourth and fifth planes at dihedral angles of substantially 125* 16'', said second, third, fourth and fifth planes each being defined by a pair of opposing edges and an included edge, each included edge joining adjacent coplanar edges at 120* and the edges intersecting at said points joining at 90*.
 11. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of linear strut members extending from each junction of said straight edges at the periphery forming a fully triangulated interior framework to define a saddle-like structural module, said polygonal periphery having 12 straight edges, one pair of opposing edges together with an included edge defining a first plane, a second pair of opposing edges together with an included edge defining a second plane, a third pair of opposing edges together with an included edge defining a third plane, the three remaining, non-intersecting edges defining a base plane, said first, second and third planes, intersecting said base plane, the edges of said pairs being respectively connected to said non-intersecting edges at the intersection of said planes.
 12. The module of claim 11, above, wherein the interior angle of the vertices are each substantially 120*, and the dihedral angles of said intersecting planes are substantially 109* 28''.
 13. The module of claim 11, above, wherein the interior angles of the vertices are each substantially 135*, and the dihedral angles of said intersecting planes are substantially 125*16''.
 14. A saddle-like polygonal surface module for defining, in conjunction with other, related modules, space enclosing structures, the module comprising: a nonplanar, skew polygonal periphery, having straight edges and a plurality of planar surface members extending from said straight edges at the periphery forming a fully triangulated interior surface to define a saddle-like structural module, said polygonal periphery having 12 straight edges, one pair of opposing edges together with an included edge defining a first plane, a second pair of opposing edges together with an included edge defining a second plane, a third pair of opposing edges together with an included edge defining a third plane, the three remaining, non-intersecting edges defining a base plane, said first, second and third planes, intersecting said base plane, the edges of said pairs being respectively connected to said non-intersecting edges at the intersection of said planes.
 15. The module of claim 14, above, wherein the interior angle of the vertices are each substantially 120*, and the dihedral angles of said intersecting planes are substantially 109* 28''.
 16. The module of claim 14, above, wherein the interior angles of the vertices are each substantially 135*, and the dihedral angles of said intersecting planes are substantially 125* 16''. 